bayesian geostatistical modelling of malaria and lymphatic ...concurrently, blood smears were...

Bayesian geostatistical modelling of malaria andlymphatic filariasis infections in Uganda:predictors of risk and geographical patterns ofco-endemicityStensgaard et al.

Stensgaard et al. Malaria Journal 2011, 10:298http://www.malariajournal.com/content/10/1/298 (11 October 2011)

RESEARCH Open Access

Bayesian geostatistical modelling of malaria andlymphatic filariasis infections in Uganda:predictors of risk and geographical patterns ofco-endemicityAnna-Sofie Stensgaard1,2*, Penelope Vounatsou3, Ambrose W Onapa4, Paul E Simonsen2, Erling M Pedersen2,Carsten Rahbek1 and Thomas K Kristensen2

Abstract

Background: In Uganda, malaria and lymphatic filariasis (causative agent Wuchereria bancrofti) are transmitted bythe same vector species of Anopheles mosquitoes, and thus are likely to share common environmental risk factorsand overlap in geographical space. In a comprehensive nationwide survey in 2000-2003 the geographicaldistribution of W. bancrofti was assessed by screening school-aged children for circulating filarial antigens (CFA).Concurrently, blood smears were examined for malaria parasites. In this study, the resultant malariological data areanalysed for the first time and the CFA data re-analysed in order to identify risk factors, produce age-stratifiedprevalence maps for each infection, and to define the geographical patterns of Plasmodium sp. and W. bancroftico-endemicity.

Methods: Logistic regression models were fitted separately for Plasmodium sp. and W. bancrofti within a Bayesianframework. Models contained covariates representing individual-level demographic effects, school-levelenvironmental effects and location-based random effects. Several models were fitted assuming different randomeffects to allow for spatial structuring and to capture potential non-linearity in the malaria- and filariasis-environment relation. Model-based risk predictions at unobserved locations were obtained via Bayesian predictivedistributions for the best fitting models. Maps of predicted hyper-endemic malaria and filariasis were furthermoreoverlaid in order to define areas of co-endemicity.

Results: Plasmodium sp. parasitaemia was found to be highly endemic in most of Uganda, with an overallpopulation adjusted parasitaemia risk of 47.2% in the highest risk age-sex group (boys 5-9 years). High W. bancroftiprevalence was predicted for a much more confined area in northern Uganda, with an overall population adjustedinfection risk of 7.2% in the highest risk age-group (14-19 year olds). Observed overall prevalence of individual co-infection was 1.1%, and the two infections overlap geographically with an estimated number of 212,975 childrenaged 5 - 9 years living in hyper-co-endemic transmission areas.

Conclusions: The empirical map of malaria parasitaemia risk for Uganda presented in this paper is the first basedon coherent, national survey data, and can serve as a baseline to guide and evaluate the continuousimplementation of control activities. Furthermore, geographical areas of overlap with hyper-endemic W. bancroftitransmission have been identified to help provide a better informed platform for integrated control.

* Correspondence: [email protected] for Macroecology, Evolution and Climate, Department of Biology,University of Copenhagen, Universitetsparken 15, DK-2100 Copenhagen,DenmarkFull list of author information is available at the end of the article

Stensgaard et al. Malaria Journal 2011, 10:298http://www.malariajournal.com/content/10/1/298

© 2011 Stensgaard et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the CreativeCommons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, andreproduction in any medium, provided the original work is properly cited.

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BackgroundMalaria and lymphatic filariasis are two of the most com-mon mosquito-borne parasitic diseases worldwide. Theiroverall prevalence and health significance have madethem top priorities for global control and elimination[1,2]. To plan and evaluate such activities in a cost-effec-tive manner, reliable baseline maps of the geographicaldistribution of at-risk areas and estimates of the numberof infected individuals are important tools to guide andevaluate the continuous implementation of control activ-ities. Likewise, identifying areas of co-endemicity (geogra-phical overlap) is a main operational issue [3] for recentlyadvocated integrated control planning [3-5].In Uganda, malaria is highly endemic with tempera-

ture and rainfall allowing stable, year-round transmis-sion with relatively little seasonal variability in mostparts of the country [6]. Plasmodium falciparum is byfar the most common of the existing malaria species inUganda, contributing 90-98% of the parasite population[7,8] Despite being a leading cause of morbidity andmortality [9], only relatively few, community-based stu-dies of malaria have been carried out in Uganda[7,10,11]. Malaria risk and endemicity have previouslybeen assessed as part of global-coverage mapping pro-jects based on historical data or climatic suitability[12-16]. However, no detailed empirical risk map hasbeen developed based on coherent national survey datacollected in a standardised manner.Besides malaria, several neglected tropical diseases are

reported to be co-endemic in Uganda [11,17] amongthese bancroftian lymphatic filariasis, resulting frominfection with the mosquito-borne parasitic nematodeWuchereria bancrofti. Despite being recognized as amajor public health and socio-economic problem,knowledge about the occurrence of lymphatic filariasisin Uganda was scanty, until a school-based survey in2000-2003, allowed the geographical distribution of lym-phatic filariasis throughout the country to be mapped[18]. During the same survey, malariological data werecollected, but until now no analysis has been presentedof these data.In Uganda, as in many other tropical regions, Plasmo-

dium and W. bancrofti parasites share common mos-quito vector species [19,20]. Thus, they may not occurindependently of each other, and the risk of co-infection(multiple species infection) might be considerable. Theoutcome of parasite co-infections often differs signifi-cantly from that of single infections [21,22], and manyof the major human infections are known to be affectedby the presence of other pathogens altering diseaseseverity, levels of infection or the spatio-temporal dis-ease patterns [23-29]. Yet, only few epidemiological stu-dies explicitly address e.g. malaria-filarial co-infectionand/or co-endemicity.

In the present paper, ecological correlates and risk fac-tors of both malaria and lymphatic filariasis infections inUganda are investigated, and nation-wide risk maps aredeveloped using solid empirical survey data and model-based geostatistics.The objectives were two-fold: i) to derive statistically

robust prevalence estimates of malaria and lymphaticfilariasis infections separately at un-sampled locations(smooth prevalence maps), and ii) to determine theextent of geographical overlap (co-endemicity) of thetwo parasitic infections. Risk estimates are moreoverlinked to population data to calculate the number ofschool-aged children at risk of each infection separately,as well as the number of children living in areas of over-lapping hyper-endemic malaria and lymphatic filariasistransmission.

MethodsSurvey dataThe screenings were carried out between October 2000and April 2003 and included pupils aged 5 - 19 years ofage from Ugandan primary schools covering all majortopographical and ecological zones of the country.Details about survey design and sampling methods havealready been given elsewhere [18]. Briefly, a finger-prickblood sample (100-μl) was first collected from eachchild and examined for W. bancrofti-specific circulatingfilarial antigens (CFA) using commercial immunochro-matographic cards. When possible, and when the childagreed another (100- μl) blood sample was collected andused to prepare a thick smear to examine for infectionwith malaria parasites. Malaria parasites were identifiedto the genus level, and will hereafter be referred to asPlasmodium sp. As not every subject allowed a secondsample to be collected, the number of children exam-ined for Plasmodium sp. was slightly lower than thenumber examined for W. bancrofti antigens. In total,malariological data was available from 71 schools (totalof 11,481 pupils), whereas W. bancrofti infection datawere available from 76 schools (total of 17,533 pupils)[18,30]. Boys and girls were examined in approximatelyequal numbers. A map showing the locations of the sur-veyed schools and the raw prevalence data can be seenin Figure 1.The studies which contributed data used in this paper,

received ethical clearance from the Uganda NationalCouncil for Science and Technology and were approvedby the Central Scientific Ethical Committee of Denmark.

Environmental and population density dataSatellite sensor data on Normalized Difference Vegeta-tion Index (NDVI) and day- and night-time land surfacetemperatures from the Moderate Resolution ImagingSpectroradiometer (MODIS) satellite were obtained


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from the United States Geological Survey U.S. Geologi-cal Survey (USGS) Land Processes Distributed ActiveArchive Center (LP DAAC) [31] at 1 km resolution.NDVI, is used as a surrogate for moisture availability[32].The products were downloaded for every 8 - 16 days in

the period 2000 to 2003 and average annual compositemaps produced by combining all maps in the period2000-2003 to reduce the variation between climate years.Based on Uganda’s two principal rainy seasons, March toMay, and August to November, average wet season anddry season composite maps were similarly produced. Aclimate surface grid at 5 × 5 km resolution consisting ofmonthly long-term normal rainfall and evapotranspira-tion estimates was obtained from the IGAD/Nile Mini-mum Medical Database (MMDb) [33] and seasonal andannual averages calculated. Altitude was determinedfrom a Digital Elevation Model layer produced fromNASA’s Shuttle Radar Topography Mission (SRTM) [34].Permanent water bodies, surrounding wetlands and theirboundaries were identified through the National BiomassStudy [35] and validated using the 2000-2003 MODISsatellite products. A distance grid was developed basedon the Euclidean distance between each school and thenearest permanent surface water body.

Environmental data for model fitting were extractedusing the satellite positions of each school, as the aver-age of the environmental conditions found within a cir-cular area of 1 km buffered around each school position.A gridded population surface at 1 km2 resolution was

obtained from LandScanTM 2002 Global PopulationDatabase [36]. The percentage of boys and girls in eachage group (5-9, 10-14 and 15-19 years) out of the totalUgandan population was obtained from the 2002 data ofthe international data base of the U.S Census Bureau[37].For the purpose of predicting infection risk at unob-

served locations, a grid covering Uganda at 2 × 2 kmresolution was constructed, (resulting in approximately60,000 grid cells) and the average environmental dataextracted for each grid cell. Environmental grid data wasmanaged with ArcGIS version 9.3 (ESRI; Redlands,USA) with the Geospatial Modelling Environment(GME) extension [38]

Statistical analysisSchool-children were classified into three age groups ofapproximately equal sizes (group 1: children aged 5-9years, group 2: children aged 10-14 years and group 3:children aged 15-19 years) following Onapa et al. [18].

±BA

Prevalence (Plasmodium sp.) Prevalence (W. bancrofti) 50%

20%

Inland water bodies 0 100 20050K ilom eters

Figure 1 Maps of survey locations and observed prevalence of infections. A) Plasmodium sp. parasitaemia in 71 schools and B) Wuchereriabancrofti antigenemia in 76 schools (children aged 5-19 years) in Uganda, 2000 - 2003.


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The Pearson c2-test was used to assess associationsbetween sex and age with Plasmodium sp. and W. ban-crofti, single and mono-infections. Single infection refersto infection with a particular species irrespective ofother infections that may be present in the individual,whereas mono-infection refers to infection with only theparticular species of parasite in question.Bivariate logistic regression models for each parasitic

infection were developed to investigate the relationshipbetween the outcome variable (single infection status)and covariates (demography and environmental themes).To account for clustering at the school-level, a location-specific random effect was included in the bivariatemodels. To reduce confounding arising from correlatedenvironmental variables, significant variables within thesame environmental themes were ranked according tothe goodness of fit Akaike Information Criteria (AIC)[39] and the best fitting one selected for further model-ling. These analyses were carried out in STATA version10 (Stata, College Station, TX, USA).Environmental and demographic covariates with sig-

nificance level p < 0.15 were then built into Bayesianlogistic regression models, using the Bayesian statisticalsoftware OpenBUGS (vs 3.1.1., Imperial College & Med-ical Research Council; London, UK) [40]. For each para-site separately, two models with school-level randomeffects to take geographical dependence into accountwere fitted : i) an exchangeable model assuming thatrandom effects arise from an independent normal distri-bution with mean 0 and variance quantifying extra bino-mial variation, and ii) a geostatistical model assumingthat random effects arise from a Gaussian spatial pro-cess quantifying geographical correlation. Model fit wasimplemented via Monte Carlo methods which allowflexibility in fitting complex models and avoid asympto-tic inference and the computational problems encoun-tered in likelihood-based fitting [41]. Furthermore, asexploratory analysis (inspection of scatter plots with afitted locally weighted scatter-plot curve) indicated non-linearity between infection status and a number of cli-matic variables, models with categorized climatic vari-ables were also fitted for comparison.Model-based predictions of prevalence at unobserved

locations were obtained via Bayesian predictive distribu-tions for the models [41], using Revolution R Enterprise(vs 4.0, Revolution Analytics). Key outputs are probabil-ity distributions of the predicted prevalence at the un-sampled locations that can be summarized by a mean,standard deviation and Bayesian Credible intervals (BCI).To assess the best performing prediction model,

model fit was also carried out on a randomly selectedsubset (~80%) of the schools (training set). The remain-ing locations, comprising a simple random sample, wereused for validation (test localities). The 95% credible

interval of the posterior distribution at the test localitieswere calculated, and the best performing model for eachage group was considered the one with the highest pro-portion of test locations having observed prevalenceswithin this interval.A complete mathematical description of the models

used is given in the Additional file 1.

ResultsParasitological findingsThe observed infection status with single- or mono-infections of school-children, stratified by sex and agecan be seen in Table 1.Overall observed prevalence of single Plasmodium sp.

infection was 35.2%, ranging from 7.4% in sites in theSouthern and North-West of Uganda, to 75.5% on theeastern shore of Lake Victoria (Figure 1). Prevalencewas highest in the 5-9 year olds (43.8%), dropping to31.4% in the oldest age group. Boys were more infectedthan girls (38.9% versus 36.5%).Overall observed CFA (W. bancrofti) prevalence was

3.9% ranging from 0% in sites in the southern parts inthe country to 30.7% in the West Nile area and Northof Lake Kyoga. Prevalence was lowest in the 5-9 yearolds (2.9%) and peaked in the oldest school-children(6.3%), but there was no significant difference betweenboys and girls.The overall prevalence of co-infection was 1.1% (129

individuals out of 11,481 co-infected). In general, moreboys than girls had co-infections (72 versus 57 indivi-duals). The age group with the highest level of co-infec-tion was the 10-14 year olds (87 individuals (0.9%)).Figure 2 depicts the geographical distribution of the rawprevalence data of Plasmodium sp. and W. bancroftimono- and co-infection, with the school as the unit ofanalysis. Co-infection was observed in 20 out of 71schools, with the highest frequencies, exceeding 10%,found in schools in the northern parts of the country.

Bayesian model validationThe summary results of the model validation can beseen in Table 2, and are presented first since inferenceand final predictions are based on the best performingmodels. For malaria both the exchangeable and geosta-tistical models were able to correctly predict most of thetest locations (71 - 93%) within the 95% BCI of the pos-terior predictive distributions. However, the exchange-able model also produced the overall narrowest BCIwidths, and was thus considered the model with thebest predictive performanceFor W. bancrofti the geostatistical models were able to

predict more test locations correctly within the 95% BCI(87-93%) than the exchangeable models, and alsoshowed the narrowest overall BCIs.


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For both malaria and lymphatic filariasis the linearmodels performed as good as or better than the catego-rical models, with the linear models predicting as manyor more of the test locations correctly, and with overallnarrower BCI’s for the linear models.

Predictors of single infectionsAssociations of malaria parasitaemia and W. bancroftiantigenaemia risk with demographic and environmen-tal factors resulting from the bivariate and the Baye-sian multivariate exchangeable and geostatisticalmodels with linear terms can be seen in Table 3 andTable 4, respectively. The estimates are presented fromthe bivariate logistic regression models and Bayesianmodels with either exchangeable random effects or aspatial location specific random effect. Co-variateeffects differed markedly between the two parasiticinfections.For the Plasmodium sp., the non-spatial bivariate

logistic regression analysis and likelihood ratio testsshowed that age, sex, season of data collections and allremotely sensed factors were significant at the 15% sig-nificance level. Males and younger children had a signif-icantly higher risk of parasitaemia than females andolder children. Diurnal temperature range and precipita-tion and NDVI composited over the wet season per-formed better than the other seasonal composites asmeasured by AIC (results not shown), and was thusselected for inclusion in Bayesian multivariate models.However, only the positive relationship with NDVIremained significant in these models.The non-spatial bivariate analysis of W. bancrofti

infection revealed that age, season, elevation and allremotely sensed environmental factors were significantrisk factors. High risk was related to high average annualrainfall and low dry season NDVI. The positive

Table 1 Comparison of demographic factors associated with Plasmodium sp. and W. bancrofti single and mono-infections

Plasmodium sp. W. bancrofti

# childreninfected(%)

Schoolprevalencerange in %

Χ2 P - value # childreninfected(%)

Schoolprevalencerange in %

Χ2 P - value

Single infection

Sex

Male 2224 (38.9) 8.1 to 73.4 359 (4.1) 0 to 31.1

Female 2108 (36.5) 6.7 to 73.3 7.14 0.008 331 (3.7) 0 to 30.5 1.85 0.173

Age groups

5 to 9 1509 (43.8) 0 to 81.5 139 (2.9) 0 to 25.0

10 to 14 2417 (35.8) 0 to 76.3 419 (4.0) 0 to 34.4

15 to 19 401 (31.4) 0 to 53.2 86.6 < 0.001 132 (6.3) 0 to 49.0 44.8 < 0.001

Mono-infection

Sex

Male 2114 (37.6) 8.1 to 77.6 104 (1.8) 0 to 19.6

Female 2005 (35.4) 6.7 to 73.7 5.6 0.018 105 (1.9) 0 to 25.0 0 0.978

Age groups

5 to 9 1453 (43.0) 0 to 81.3 26 (0.8) 0 to 18.7

10 to 14 2287 (34.4) 0 to 76.1 149 (2.3) 0 to 19.5

15 to 19 379 (30.6) 0 to 61.9 93.4 < 0.001 34 (2.7) 0 to 23.8 32.6 < 0.001

C oin fec tionsPlasmodium sp.W. bancrofti N o in fections

Infection status ±

0 100 20050K ilom ete rs

In land w a te r bod ies

Figure 2 Observed distribution of mono- and co-infectionswith Plasmodium sp. and W. bancrofti. Data from 11,481 pupilsaged 5 - 19 years in 71 schools in Uganda, collected during 2000-2003.


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associations with day- and night-time temperatures andseason were no longer significant in the Bayesian multi-variate models. Older children had a significantly higherrisk of being CFA positive, whereas sex was not signifi-cant at the 15% significance level and thus not includedin the Bayesian models. The spatial decay parameter in

the geostatistical model had a posterior mean of 1.00which in the current exponential setting corresponds toa minimum distance for which the spatial correlationbecomes (less than 5%) of 3 km (95% BCI: 1.78, 4.29km)), indicating the presence of spatial autocorrelationin the filariasis data.

Table 2 Model validation summary for the exchangeable (non-spatial) and geostatistical models of i) malaria and ii)filariasis parasitaemia risk

Age group Malaria 95% BCI* (width) Filariasis 95% BCI* (width)

Exchangeable models

Linear 5-9 yrs 79% (0.60)** 87% (0.32)

10-14 yrs 86% (0.58)** 87% (0.35)

15-19 yrs 100% (0.56)** 87% (0.36)

Categorical 5-9 yrs 79% (0.64) 87% (0.37)

10-14 yrs 86% (0.62) 87% (0.42)

15-19 yrs 100% (0.65) 93% (0.45)

Geostatistical models

Linear 5-9 yrs 71% (0.61) 93% (0.15)**

10-14 yrs 86% (0.60) 93% (0.21)**

15-19 yrs 100% (0.58) 93% (0.26)**

Categorical 5-9 yrs 71% (0.66) 87% (0.28)

10-14 yrs 86% (0.65) 87% (0.36)

15-19 yrs 100% (0.67) 93% (0.35)

For each model, the table shows the percentage of test locations with observed prevalence falling within the 95% Bayesian credible intervals of the posteriorpredictive distribution and the corresponding BCI width.

Linear and categorical refers to models with co-variates in either linear or categorized form.

** model with the highest percentage of test localities with observed prevalence falling within the 95% BCI and overall narrowest BCI width.

Table 3 Malaria parasitaemia risk factors as identified from single infection bivariate non-spatial and Bayesianmultivariate exchangeable and geostatistical models (N = 11,481)

Covariates Bivariate logistic regression model(non-spatial)OR 95% CI

Bayesian logistic regression model(exchangeable)OR 95% BCI*

Bayesian geostatistical model(spatial)

OR 95% BCI*

Age group (5 - 9 yrs) 1.00 1.00 1.00

10 - 14 yrs 0.67 (0.60 - 0.73) 0.66 (0.60 - 0.73) 0.66 (0.60 - 0.72)

15 - 19 yrs 0.55 (0.47 - 0.63) 0.55 (0.46 - 0.64) 0.54 (0.47 - 0.64)

Sex (female) 1.00 1.00 1.00

Male 1.12 (1.03 - 1.21) 1.14 (1.05 - 1.23) 1.14 (1.05 - 1.23)

Season (dry) 1.00 1.00 1.00

Wet 2.30 (1.54 - 3.44) 2.23 (1.43 - 3.23) 2.33 (1.50 - 3.53)

NDVI (wet season) 1.03 (1.01 - 1.04) 1.02 (1.00 - 1.05) 1.02 (1.00- 1.05)

Precipitation (wetseason)

1.01 (1.00 - 1.02) 1.00 (0.99 - 1.01) 1.00 (0.99 - 1.01)

LST diurnal range(annual)

0.94 (0.88 - 0.99) 1.04 (0.95 - 1.14) 1.04 (0.95 - 1.15)

Mean (95% BCI) Mean (95% BCI)

τ2 (non-spatialvariance)

- 2.00 (1.34 - 2.82)

s (spatial variance) - 0.53 (0.36 - 0.77)Range (in km) - 0.08 (0.02 - 0.65)

Results are presented as odds ratios (OR) with their respective confidence intervals (95% CI) or Bayesian credible intervals (95% BCI). NDVI, normalized differencevegetation index; LST, land surface temperature. Range indicates the distance at which spatial correlation is lower than 5%.


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Prediction of Plasmodium sp. and W. bancrofti singleinfectionsThe best performing models according to the modelvalidation procedure were employed to predict infectionrisk at the un-sampled locations represented by the app.60,000 grid cells across Uganda. The predicted riskmaps of single malaria and lymphatic filariasis infectionsare shown in Figure 3 and Figure 4, respectively.Since age remained a significant risk factor for both

malaria and lymphatic filariasis after adjusting for con-founding factors and spatial correlation, prediction mapswere developed for each age group separately. Formalaria this was also the case for gender. The spatialpatterns were identical for each age-sex group, thoughthe proportion infected with Plasmodium sp. was lowerfor girls and older children, and the proportion infectedwith W. bancrofti lower for younger children. Risk mapsfor all age-sex groups are available from the correspond-ing author upon request.

Estimating the numbers infectedThe age and sex stratified 2002 population surfaces wasmultiplied with gridded surfaces of the prediction mod-els representing the mean and the lower and upper 95%BCI of the predicted prevalence in each age-sex group,for each parasite infection separately. The resulting

layers gave maps of the predicted number of infectedchildren per km2 and summarizing across the wholestudy area gave the total number of infected children ineach age-sex group in Uganda. The estimated numberof children at risk in the respective age-sex groups ispresented in Table 5, along with the population adjustedprevalence for each age-sex group. The total predictednumber of school-children per km2 with either malariaor filarial parasites is illustrated in Figure 5A and Figure5B, respectively.

Co-endemicity mappingThe predicted prevalence maps for malaria and W. ban-crofti single-infections were superimposed to identifygeographical areas where hyper-endemic malaria (>50%) and hyper-endemic lymphatic filariasis (> 10%)overlap in Uganda. Figure 6 shows the resultant co-endemicity map for children aged 5 - 9 years. The lar-gest areas of hyper co-endemicity were located in Aruadistrict in northwestern Uganda, Kitgum District innorthern Uganda and more scattered areas found on thenorthern side of Lake Kyoga, central Uganda. Based onthis map 212,975 children aged 5 - 9 years were esti-mated to be living in areas of concomitant hyper-ende-mic malaria and lymphatic filariasis in Uganda, and thusat risk of co-infection.

Table 4 Lymphatic filariasis antigenemia risk factors as identified from single infection bivariate non-spatial andBayesian multivariate exchangeable and geostatistical models (N = 17,533)

Covariates Bivariate logistic regression model(non-spatial)OR 95% CI

Bayesian logistic regression model(exchangeable)OR 95% BCI*

Bayesian geostatistical model(spatial)

OR 95% BCI*

Age group (5 - 9yrs)

1.00 1.00 1.00

10 - 14 yrs 2.04 (1.65, 2.55) 2.11 (1.69, 2.61) 2.13 (1.70, 2.64)

15 - 19 yrs 2.47 (1.88, 3.25) 2.53 (1.90, 3.31) 2.54 (1.91, 3.31)

Season (dry) 1.00 1.00 1.00

Wet 3.86 (0.66 - 22.4) 4.24 (0.55, 13.65) 3.38 (0.99, 7.94)

NDVI (dry season) 0.93 (0.87, 0.99) 0.91 (0.89, 0.94) 0.90 (0.86, 0.93)

Precipitation(annual)

1.04 (1.00, 1.09) 1.06 (1.02, 1.09) 1.06 (1.03, 1.09)

LST (day, dry) 1.48 (1.17, 1.86) 1.13 (0.95, 1.36) 1.20 (0.90, 1.22)

LST (night, dry) 2.56 (1.55, 4.25) 1.42 (0.95, 2.01) 1.22 (0.83, 1.79)

Altitude (< 1.050m)

1.050 - 1.150 0.26 (0.04, 1.71) 0.66 (0.06, 2.81) 0.15 (0.01, 0.71)

1.150-1.250 0.06 (0.01, 0.49) 0.17 (0.01, 0.84) 0.28 (0.02, 1.82)

> 1.250 0.01 (0.00, 0.14) 0.15 (0.03, 0.76) 0.21 (0.02, 0.93)

Mean (95% BCI) Mean (95% BCI)

τ2 (non-spatialvariance)

- 0.15 (0.08, 0.26) -

s (spatial variance) - - 4.34 (2.25, 8.80)Range (in km) - - 2.98 (1.78, 4.29)

Results are presented as odds ratios (OR) with their respective confidence intervals (95% CI) or Bayesian credible intervals (95% BCI); NDVI, normalized differencevegetation index; LST, land surface temperature. Range indicates the distance at which spatial correlation is lower than 5%.


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±BA

< 3031- 3536 - 4041 - 4545 - 50> 50

< 1515 - 1617 - 18> 18

Predicted prevalence of infection (%)SD of predicted prevalence (%)

School locations0 100 20050K ilom eters Inland water bodies

Figure 3 Map of predicted malaria prevalence. A) Predicted Plasmodium sp. parasitaemia risk for schoolchildren in the highest risk group (5-9years old boys) and B) associated map of the standard deviation of the predicted risk.

±BA

< 11 - 56 - 1011 - 2526 - 50> 50

< 56 - 1516- 20> 25

Predicted prevalence of infection (%)SD of predicted prevalence (%)

School locations0 100 20050K ilom eters Inland water bodies

Figure 4 Map of predicted lymphatic filariasis prevalence. A) shows predicted W. bancrofti antigenemia risk for school-children in thehighest risk age group (14-19 years) and B) shows the associated map of the standard deviation of the predicted risk.


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Table 5 Estimated numbers of children infected with a) Plasmodium sp. and b) W. bancrofti filarial parasites in Ugandain 2002

Age-sexgroup

Estimatedpopulation

Estimated number ofinfected children

Lower 95%BCI*

Upper 95%BCI*

Model basedprevalence

Model-based populationadjusted prevalence

a)Plasmodiumsp.

Boys 5-9 yrs 1,966,324 927,634 337,740 1,547,775 47.7% (4.5) 47.2%

Boys 10-14yrs

1,587,915 607,356 190,873 1,128,372 38.8% (4.3) 38.2%

Boys 14-19yrs

1,268,729 431,452 125,464 848,679 34.6% (4.1) 34.0%

Girls 5-9 yrs 1,956,764 607,291 163,873 1,252,415 31.5% (3.5) 31.0%

Girls 10-14yrs

1,576,155 372,161 90,670 852,659 24.1% (3.3) 23.6%

Girls 14-19yrs

1,247,670 254,625 55,329 614,181 21.0% (3.0) 20.4%

TOTAL 9,603,557 3,200,519 963,949 6,244,081 33.0% 33.3%

b) W.bancrofti

5-9 yrs 3,923,088 170,668 5,027 691,754 6.7% 4.4%

10-14 yrs 3,164,070 202,885 8,416 733,247 9.3% 6.4%

14-19 yrs 2,516,399 180,860 7,893 665,842 10.1% 7.2%

TOTAL 9,603,557 554,413 21,336 2,090,843 8.7% 6.0%

* Bayesian credible interval

Figure 5 Maps of the estimated at-risk populations in Uganda, 2002. The maps show the estimated numbers of school-children aged 5-19years per km2 infected with Plasmodium sp. parasites (A) and W. bancrofti filarial parasites (B)


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DiscussionWith recent advances in geospatial tools and spatial sta-tistics, studies analysing the relationship between infec-tion dynamics and ecological factors have given newinsights into the ecology and epidemiology especially ofmalaria [13,15,42] - but also lymphatic filariasis [43,44].The accurate geographical identification and enumera-tion of individuals at risk of single-species infection, theoutcome of such studies, is an important component incontrol efforts, facilitating a better resource allocation,health management and targeted interventions toachieve the highest risk reduction for the most popu-lated areas.In the present study, nationally representative survey

data of malaria and lymphatic filariasis in Uganda wereapplied to identify significant predictors associated withparasitaemia and antigenaemia risk. Model-based infec-tion risk maps for 2002 were produced and the numberof infected children estimated for three different agegroups.The map of malaria is the first for Uganda based on

empirical data sampled in a standardised and coherentmanner. The survey locations are randomly chosen andthe data are available at individual level allowing forestimation of age-specific risk, as well as adjusting forseasonality. Even though the data were collected during2000-2003, the maps produced still represent the mostup-to-date and detailed maps of malaria and lymphaticfilariasis risk in the country. On-going LF and malaria

control initiatives in Uganda are likely to have changedthe patterns, thus the maps can serve as an importantbaseline to guide and evaluate the continuous controlimplementation.Prior to the present analysis, historical malariological

data were compiled by the MAP (Malaria Atlas Project)[45] and MARA (mapping malaria risk in Africa) pro-jects and used to prepare parasitaemia risk maps at highresolution. For example, Craig et al [12] developed a cli-matic suitability malaria risk map for the whole ofAfrica, and the first empirical based map for Ugandawas produced by Hay et al [13] as part of a global riskmap based on historical data to define the spatial limitsof malaria within all endemic countries. However, oftenhistorical survey data are not representative as high riskareas tend to be over-represented, and surveys at differ-ent locations are conducted with different methodology,making direct comparisons between maps difficult.The first risk map of lymphatic filariasis in Uganda

was produced by Onapa et al [18] based on the samesurvey data as used the current study. In this study, itwas estimated that 8.7 million people (all age groups)lived in areas with > 1% CFA prevalence, and 5.9 millionlived in areas with more than 5% CFA prevalence [18].Here, this mapping is improved upon by using model-based geostatistical analysis to predict for each pixel inthe map the risk of having CFA stratified according toage as well as producing a map of the associated predic-tion errors. Bayesian inference and MCMC simulation isapplied as this is the only way these highly parameter-ized spatial models can be estimated [46]. Furthermore,the modelling approach applied in the current studyallowed estimation of the actual number of school-agedchildren in each age group expected to be CFA positive.However, as the data was collected over a three-yearperiod (2000-2003), the estimated numbers of infectedis likely to diverge from 2002 real numbers.Bayesian geostatistical modelling has previously been

applied to lymphatic filariasis data in Haiti [47,48], WestAfrica [28] and Papua New Guinea [49], however thesestudies did not aim to predict risk estimates and pro-duce smooth maps of disease risk.More commonly, Bayesian geostatistical modelling has

been applied to malaria data and used to estimate para-sitaemia risk for a number of countries and regions inAfrica, including amongst others West and CentralAfrica [50-52], Angola [53], Tanzania [54], Kenya [55],Zambia [56] and Somalia [57].An important advantage of Bayesian geostatistical ana-

lysis is that it takes the spatial correlation often presentin many epidemiological data sets into account andmodel the effects of the co-variates and spatial correla-tion, if present, simultaneously. If spatial correlation ispresent the independence assumption central to

±

0 100 20050K ilom ete rs

No hyper-endem ic transmissionPlasm odium sp . (>50% )W. bancrofti (>10% )Overlap

Co-endemicity (hyper)

< 11 - 56 - 13

Observed co-infection (%)

In land w a te r bod ies

Figure 6 Map showing areas of hyper-endemic malaria (red)and W. bancrofti infections (green) and their geographicaloverlap (blue) for children aged 5-9 years in Uganda. Hyper-endemicity is defined as >50% prevalence of Plasmodium sp.infection and >10% W. bancrofti infection prevalence.


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generalized linear model theory is violated, which couldpotentially lead to imprecise risk estimates, predictionerrors and wrong estimation of the significance of therisk factors.The geostatistical model of W. bancrofti infection esti-

mated a spatial correlation with a minimum distance atwhich spatial correlation becomes negligible of ~ 3 km.In accordance with this the spatial models also outper-formed the non-spatial LF models in terms of numberof test locations captured within the 95% posterior cred-ible intervals and their widths. In line with our findings,Alexander et al [58] found that the spatial correlation ofW. bancrofti in Papua New Guinea was reduced by halfover a distance of 1.7 km and Boyd et al found that thedistance beyond which remaining spatial correlation isassumed to be negligible to be 2.15 km for W. bancroftiin school-children in Leogane, Haiti [59].The malaria data analysed in the present study on the

other hand, showed signs of very weak spatial correla-tion. Thus attempting to model the spatial correlationcould lead to increased number of model parameterswhile decreasing the precision of the estimates. TheBayesian geostatistical model developed estimated alower spatial correlation than the pixel size used for pre-diction (2 × 2 km) indicating that spatial correlation isonly present at very local scales. Validation confirmedthat the fitted non-spatial malaria models were superiorto the fitted spatial models. A similar result was foundby Riedel et al [56] when mapping malaria risk usingthe Zambia national indicator survey data. Other studiesalso reported very small scale of spatial variation ofmalaria [58,60,61]. For example, Thompson et al foundthe risk of malaria varying by a factor of 6 over 500 m[62], while Alexander et al found distance over whichthe correlation reduces by half to be only 14 meters[58].The much smaller scale of variation of malaria could

be related to its rapid variation in infection over time.One infective mosquito bite results in patent infectionabout two weeks later. By comparison, the patent periodis about one year for W. bancrofti infections, which alsolast much longer and the risk of infection per mosquitobite is much smaller [63].Besides from mapping, important common environ-

mental risk factors for malarial and filarial infections inUganda have been highlighted. For both malaria andlymphatic filariasis, the bivariate analysis indicated thatthe season the data was collected in was important withthe wet season months having higher disease risk. How-ever, in the multivariate models this relationship onlyremained significant for malaria reflecting the strongerseasonality of malaria transmission.As also presented by Onapa et al [18] older age

groups were significantly more at risk of being CFA

positive. The opposite relationship was observed forPlasmodium sp. infections, with the youngest age-groupbeing significantly more at risk. This was also the find-ings of Pullan et al [7] in a recent survey of malaria andits risk factors in four villages in Tororo district, EasternUganda. Similar to our findings, they also found thatboys were significantly more at risk than girls.

Co-endemicity of malaria and lymphatic filariasisIn contrast to the well-characterized patterns of singleparasite infections, we know surprisingly little about thepatterns and risk factors of co-endemicity and co-infec-tion of e.g. malaria and helminth infections, despitepoly-parasitism being common among populations indeveloping countries [64]. Co-endemicity is of consider-able public health importance and offers opportunitiesto enhance cost-effectiveness through combined control[3]. The identification and enumeration of individualsliving in areas where multiple diseases co-exist isemphasised, since they are at high risk of co-infections,and thus likely to suffer from co-morbidity [65].In Uganda, the same species of Anopheles mosquitoes

transmit malaria and lymphatic filariasis [18,30] andconcomitant infections in humans are likely to occurwhen the prevalence of both parasites is high [19]. Inthe present study, maps of single infection risk formalaria and lymphatic filariasis were used to identifygeographical areas of overlapping hyper-endemictransmission.A substantial geographical overlap was observed, with

an estimated 212,975 children between five and nineyears of age living in areas that are hyper-endemic formalaria and lymphatic filariasis (blue area in Figure 6).Future surveys should aim at covering these presentlyun-sampled areas, since the risk of co-infection herewould be expected to be substantial.The geographical distribution of lymphatic filariasis in

Uganda was expected to overlap with that of malaria, inparticular in very high malaria transmission areas wherethe density of the transmitting mosquitoes is expectedto be high. Surprisingly however, the distribution of W.bancrofti antigenaemia is not fully overlapping withhyper-endemic malaria areas (Figure 6), despite most ofUganda being highly endemic for malaria,A possible explanation for this pattern could be that

in some locations, even though data were collected dur-ing wet season months, those years and locations werefound to be exceptionally dry for the season. This couldhave impacted the observed prevalence of malariaresulting in lower than usual number of infections;whereas lymphatic filariasis with its much longer prepa-tent period would remain unchanged even in a dry year.It could also be partly due to the difference in “highprevalence age groups” between the two infections, with


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far the majority of CFA positives found in age group 15-19 years, the age group with the lowest observed malariainfection.Some studies have also shown that the intensity of P.

falciparum is generally lower in microfilaremic indivi-duals compared to amicrofilaraemic individuals [66] andthat filarial infections may have either benign or sup-pressive effects on malaria development [67]. Thus, thetwo parasites might interact both within the humanpopulations and the vector in ways that may alter thedynamics of transmission [19,68] and ultimately the geo-graphical patterns of co-endemicity.

ConclusionsThe age-sex stratified risk maps of malaria and lympha-tic filariasis presented here for Uganda are based onnational, coherent survey data collected during 2000-2003 and rigorous Bayesian geostatistical modelling andprediction. They can serve as an important baseline toguide and evaluate the continuous implementation ofsingle infection control activities. The maps werefurthermore used to identify areas of hyper- and co-endemicity to help provide a better informed platformfor integrated control.Parasitic co-infection and interaction phenomena in

human populations are complex and our understandingof the mechanisms by which interactions between para-sites occur and the public health implications is still lim-ited. Further studies on malaria-filarial co-infection, co-occurrence, prevalence and species interactions in var-ious geographical settings are clearly warranted. Besidesthe immediate public health implications, identifyinghigh-prevalence zones of human parasitic infections andtheir spatial overlap may also help generate new insightsand hypotheses regarding their interrelationships andtransmission.

List of abbrevationsLF: Lymphatic filariasis; CFA: circulating filarial anti-gens; NDVI: Normalized difference vegetation index;MCMC: Markov Chain Monte Carlo; LST: land surfacetemperature; BCI: Bayesian credible interval.

Additional material

Additional file 1: Additional information regarding modelformulation. Supporting information on Bayesian model formulation formalaria and lymphatic filariasis,

AcknowledgementsThe authors would like to express their gratitude to all the children whoparticipated in the surveys and to the teachers, school administrators, eldersand local leaders who facilitated the study in one way or another. Alsothanked are the district education officers and the district directors of health

services, who provided personnel and facilities to assist the survey teams.The staff of the Vector Control Division, particularly A. Auma, G. Egitat, C.Elamu and J. Kirunda, were instrumental in executing the field phase of thisstudy, often under difficult circumstances, and C. Adikinyi and A. Ebinemanaged the data entry. The study received financial support from theDanish Bilharziasis Laboratory, Denmark. PV (project no. 325200-118379) isgrateful to the Swiss National Science Foundation (SNF) for financial support.AS is supported by a PhD studentship partly funded by DHI Denmark. CRand AS thank the Danish National Research Foundation for its support ofthe Center for Macroecology, Evolution and Climate. TKK is supported bythe CONTRAST project (http://www.eu-contrast.eu) funded by EuropeanUnion grant, FP6-STREP-2004-INCO-DEV Project no. 032203

Author details1Center for Macroecology, Evolution and Climate, Department of Biology,University of Copenhagen, Universitetsparken 15, DK-2100 Copenhagen,Denmark. 2DBL - Centre for Health Research and Development, Faculty ofLife Sciences, University of Copenhagen, Thorvaldsensvej 57, DK-1871Frederiksberg C, Denmark. 3Department of Public Health and Epidemiology,Swiss Tropical and Public Health Institute, Socinstrasse 57, P.O. Box CH-4002Basel, Switzerland. 4Vector Control Division, Ministry of Health, P.O. Box 1661,Kampala, Uganda.

Authors’ contributionsAS and AWO conceived the idea for the present study. AS analysed the dataand drafted the manuscript. PV was responsible for the conception anddesign of the statistical analysis and supervised the implementation. AWO,PES and EMP designed and carried out the parasitological surveys andprovided important intellectual content to the study. CR and TKK gavecritical input and re-appraisal in the manuscript. All authors read andapproved the final manuscript.

Competing interestsThe authors declare that they have no competing interests.

Received: 19 July 2011 Accepted: 11 October 2011Published: 11 October 2011

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doi:10.1186/1475-2875-10-298Cite this article as: Stensgaard et al.: Bayesian geostatistical modellingof malaria and lymphatic filariasis infections in Uganda: predictors ofrisk and geographical patterns of co-endemicity. Malaria Journal 201110:298.

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AbstractBackgroundMethodsResultsConclusions

BackgroundMethodsSurvey dataEnvironmental and population density dataStatistical analysis

ResultsParasitological findingsBayesian model validationPredictors of single infectionsPrediction of Plasmodium sp. and W. bancrofti single infectionsEstimating the numbers infectedCo-endemicity mapping

DiscussionCo-endemicity of malaria and lymphatic filariasis

ConclusionsList of abbrevationsAcknowledgementsAuthor detailsAuthors' contributionsCompeting interestsReferences

bayesian geostatistical modelling of malaria and lymphatic ...concurrently, blood smears were...

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